Thermodynamics and Thermochemistry - Result Question 81
####6. 5 moles of an ideal gas at $100 K$ are allowed to undergo reversible compression till its temperature becomes $200 K$. If $C _V=28 JK^{-1} mol^{-1}$, calculate $\Delta U$ and $\Delta p V$ for this process. $\left(R=8.0 JK^{-1} mol^{-1}\right)$
(2019 Main, 8 April II)
(a) $\Delta U=2.8 kJ ; \Delta(p V)=0.8 kJ$
(b) $\Delta U=14 J ; \Delta(p V)=0.8 J$
(c) $\Delta U=14 kJ ; \Delta(p V)=4 kJ$
(d) $\Delta U=14 kJ ; \Delta(p V)=18 kJ$
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Solution:
- Given,
$$ \begin{aligned} n & =5 mol, T _2=200 K, T _1=100 K \ C _V & =28 JK^{-1} mol^{-1} \ \Delta U & =n C _V \Delta T \ & =n C _V\left(T _2-T _1\right) \ & =5 mol \times 28 JK^{-1} mol^{-1} \times(200-100) K \ & =14,000 J=14 kJ \ \Delta p V & =n R \Delta T \ & =n R\left(T _2-T _1\right) \ & =5 mol \times 8 JK^{-1} mol^{-1} \times(200-100) K \ & =4000 J=4 kJ \end{aligned} $$
